International Conference on Cryptology and Information Security in Latin America

LATINCRYPT 2015: Progress in Cryptology -- LATINCRYPT 2015 pp 269-294

Twisted Hessian Curves

Conference paper

DOI: 10.1007/978-3-319-22174-8_15

Volume 9230 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Bernstein D.J., Chuengsatiansup C., Kohel D., Lange T. (2015) Twisted Hessian Curves. In: Lauter K., Rodríguez-Henríquez F. (eds) Progress in Cryptology -- LATINCRYPT 2015. LATINCRYPT 2015. Lecture Notes in Computer Science, vol 9230. Springer, Cham


This paper presents new speed records for arithmetic on a large family of elliptic curves with cofactor 3: specifically, \(8.77\mathbf{M}\) per bit for 256-bit variable-base single-scalar multiplication when curve parameters are chosen properly. This is faster than the best results known for cofactor 1, showing for the first time that points of order 3 are useful for performance and narrowing the gap to the speeds of curves with cofactor 4.


EfficiencyElliptic-curve arithmeticDouble-base chainsFast arithmeticHessian curvesComplete addition laws

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTechnische Universiteit EindhovenEindhovenThe Netherlands
  2. 2.Department of Computer ScienceUniversity of Illinois at ChicagoChicagoUSA
  3. 3.Institut de Mathématiques de MarseilleAix-Marseille UniversitéMarseille Cedex 09France